Combinatorial constructions of low-density parity-check codes for iterative decoding

Bane Vasic, Olgica Milenkovic

Research output: Contribution to journalArticlepeer-review

198 Scopus citations


This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

Original languageEnglish (US)
Pages (from-to)1156-1176
Number of pages21
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2004


  • Cyclic difference families
  • Iterative decoding
  • Low-density parity-check (LDPC) codes
  • Pasch configurations

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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